Attention-Augmented LSTM Feed-Forward Compensation for Lever-Arm-Induced Velocity Errors in Transfer Alignment

In a mother-child underwater bio-inspired robotic system, the equivalent lever arm between the master and slave inertial navigation systems (INSs) varies with launcher attitude changes and structural flexure. This time-varying lever arm introduces hard-to-model systematic velocity errors that degrade the accuracy and filter convergence of velocity difference-based transfer alignment. Traditional rigid body compensation relies on precise, constant lever-arm parameters and fails when booms, launch tubes, or flexible manipulators undergo appreciable deformation or reconfiguration. To address this, we augment a "velocity-attitude joint matching and innovation-based adaptive Kalman filter (AKF)" framework with an attention-based Long Short-Term Memory (LSTM) feed-forward module. Using only a short, real-time Inertial Measurement Unit (IMU) sequence from the slave INS, the module predicts and compensates the velocity bias induced by the lever arm. Numerical simulations of an underwater bio-inspired robot deployment scenario show that, under typical maneuvers (acceleration, turning, fin-flapping, and S-curve), the proposed method reduces the root-mean-square (RMS) misalignment angle error from about 14.5' to 5.2' and the RMS installation error angle from 8.8' to 3.0'-average reductions of about 64% and 66%, respectively-substantially improving the robustness and practical applicability of transfer alignment under time-varying lever arms and flexible disturbances.